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Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

In 1611, Kepler proposed that close packing (either cubic or hexagonal close packing, both of which have maximum densities of pi/(3sqrt(2)) approx 74.048%) is the densest ...

What space-filling arrangement of similar cells of equal volume has minimal surface area? This questions arises naturally in the theory of foams when the liquid content is ...

The funnel surface is a regular surface and surface of revolution defined by the Cartesian equation z=1/2aln(x^2+y^2) (1) and the parametric equations x(u,v) = ucosv (2) ...

A surface of revolution is a surface generated by rotating a two-dimensional curve about an axis. The resulting surface therefore always has azimuthal symmetry. Examples of ...